The Flexural Vibrations of Thin Cylinders

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The flexural vibrations of the walls of thin cylinders are considered. In this type of vibration many forms of nodal pattern may exist owing to the combination of circumferential and axial nodes. Theoretical expressions are developed for the natural frequencies of cylinders with freely-supported and fixed ends and a comparison is made with the frequencies obtained experimentally. In practice, the ends of cylinders are subjected to a certain degree of fixing by end-plates, flanges, etc., and the natural frequencies thus lie between the corresponding values for freely-supported and fixed ends. To make possible the estimation of such frequencies, a method is devised in which an equivalent wavelength factor is used. This factor represents the wavelength of the freely-supported cylinder that would have the same frequency as the cylinder under consideration when vibrating in the same mode. The results of experimental investigations with various end thicknesses and flange dimensions are recorded, and from these the equivalent factors are derived. Sets of curves calculated for cylinders with freely-supported ends and covering a range of cylinder thicknesses are given. From these it is possible to obtain close approximation to the frequencies of cylinders under other end conditions by the use of an appropriate factor. An example is given of frequency calculations for a large air-receiver for which two frequencies were identified by experiment.